Csajbók, Bence and Marino, Giuseppe and Polverino, Olga and Zullo, Ferdinando (2018) A characterization of linearized polynomials with maximum kernel. Finite Fields and their Applications. ISSN 1071-5797 (In Press)
|
Text
charmaxker-submitted2.pdf Download (389kB) | Preview |
Abstract
We provide sufficient and necessary conditions for the coefficients of a q-polynomial f over GF(q^n) which ensure that the number of distinct roots of f in GF(q^n) equals the degree of f. We say that these polynomials have maximum kernel. As an application we study in detail q-polynomials of degree q^(n-2) over GF(q^n) which have maximum kernel and for n<7 we list all q-polynomials with maximum kernel. We also obtain information on the splitting field of an arbitrary q-polynomial. Analogous results are proved for q^s-polynomials as well, where gcd(s,n) = 1.
| Item Type: | Article |
|---|---|
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria |
| Depositing User: | Bence Csajbók |
| Date Deposited: | 24 Sep 2019 13:53 |
| Last Modified: | 03 Apr 2023 06:33 |
| URI: | http://real.mtak.hu/id/eprint/100771 |
Actions (login required)
 |
Edit Item |
